# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/intExtension/INT__SGN__CLAUSES_c0', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/intExtension/INT__SGN__CLAUSES_c0', aHLu_FALSITY)).
fof(5, axiom,![X6]:![X7]:((((s(t_h4s_integers_int,h4s_intextensions_sgn(s(t_h4s_integers_int,X6)))=s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))&p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))))=>p(s(t_bool,X7)))&(((s(t_h4s_integers_int,h4s_intextensions_sgn(s(t_h4s_integers_int,X6)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))&s(t_h4s_integers_int,X6)=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))=>p(s(t_bool,X7)))&((s(t_h4s_integers_int,h4s_intextensions_sgn(s(t_h4s_integers_int,X6)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))&p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,X6)))))=>p(s(t_bool,X7)))))=>p(s(t_bool,X7))),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_intExtensions_INTu_u_SGNu_u_CASES0)).
fof(6, axiom,![X6]:?[X8]:((p(s(t_bool,X8))<=>s(t_h4s_integers_int,X6)=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))&s(t_h4s_integers_int,h4s_intextensions_sgn(s(t_h4s_integers_int,X6)))=s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,X8),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_intExtensions_SGNu_u_def)).
fof(16, axiom,![X11]:(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_nums_num,X11)=s(t_h4s_nums_num,h4s_arithmetics_zero)),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_numerals_numeralu_u_distribu_c17)).
fof(17, axiom,![X11]:![X12]:(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X11)))=s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X12)))))<=>(s(t_h4s_nums_num,X11)=s(t_h4s_nums_num,h4s_nums_0)&s(t_h4s_nums_num,X12)=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_integers_INTu_u_EQu_u_CALCULATEu_c2)).
fof(18, axiom,![X11]:(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,h4s_arithmetics_zero)<=>p(s(t_bool,f))),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_numerals_numeralu_u_equ_c1)).
fof(21, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(22, axiom,![X9]:![X13]:![X14]:s(X9,h4s_bools_cond(s(t_bool,f),s(X9,X14),s(X9,X13)))=s(X9,X13),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_bools_CONDu_u_CLAUSESu_c1)).
fof(23, axiom,![X9]:![X13]:![X14]:s(X9,h4s_bools_cond(s(t_bool,t),s(X9,X14),s(X9,X13)))=s(X9,X14),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_bools_CONDu_u_CLAUSESu_c0)).
fof(62, axiom,![X11]:![X12]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X12))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X11)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X11))),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_integers_INTu_u_LT)).
fof(64, axiom,![X10]:![X6]:(s(t_h4s_integers_int,X6)=s(t_h4s_integers_int,X10)|(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X10))))|p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X10),s(t_h4s_integers_int,X6)))))),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_integers_INTu_u_LTu_u_TOTAL)).
fof(67, axiom,![X11]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(74, axiom,s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_integers_INTu_u_NEGu_u_0)).
fof(76, axiom,![X6]:s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))=s(t_h4s_integers_int,X6),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_integers_INTu_u_ADDu_u_RID)).
fof(79, axiom,![X10]:![X6]:(~(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X10)))))<=>p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X10),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_intu_u_ariths_notu_u_less)).
fof(92, axiom,![X11]:s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_arithmetics_BIT10)).
fof(95, axiom,![X6]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X6)))=s(t_h4s_nums_num,X6),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(104, axiom,![X10]:![X6]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X10)))))=s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,X10))),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_integers_INTu_u_LTu_u_ADDR)).
fof(109, axiom,![X10]:![X6]:~((p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X10))))&p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X10),s(t_h4s_integers_int,X6)))))),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_integers_INTu_u_LTu_u_ANTISYM)).
fof(110, axiom,![X6]:s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,X6)))=s(t_h4s_integers_int,X6),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_integers_INTu_u_ADDu_u_LID)).
fof(112, axiom,![X11]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X11)))))=s(t_bool,t),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_numerals_numeralu_u_ltu_c0)).
fof(119, axiom,![X1]:(s(t_bool,f)=s(t_bool,X1)<=>~(p(s(t_bool,X1)))),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(122, axiom,![X6]:s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,X6)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_integers_INTu_u_MULu_u_LZERO)).
fof(124, axiom,![X11]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ah4s_numerals_numeralu_u_lteu_c1)).
fof(133, conjecture,![X6]:(s(t_h4s_integers_int,h4s_intextensions_sgn(s(t_h4s_integers_int,X6)))=s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))<=>p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))))),file('i/f/intExtension/INT__SGN__CLAUSES_c0', ch4s_intExtensions_INTu_u_SGNu_u_CLAUSESu_c0)).
# SZS output end CNFRefutation
